High-temperature superconductors were discovered 25 years ago. Despite the flurry of theoretical activity that followed, no textbook-like consensus on the mechanism of superconductivity has clearly emerged. This is likely due to the fact that even the simplest models proposed to describe these materials are too hard to solve. But in the last ten years, theoretical methods have been developed that capture the essential phenomena occuring in high-Tc cuprates and other exotic superconductors: Quantum cluster methods. These are a family of theoretical tools to study lattice models of interacting electrons, such as the Hubbard model. Examples are the Cluster Dynamical Mean Field Theory and the Variational Cluster Approximation. In this talk I will explain one or two of these methods and describe their application to the Hubbard model. We will see how superconductivity can emerge from a strong electron repulsion, via antiferromagnetism. I will also discuss the possible existence of a spin liquid state in simple lattice models of interacting electrons.

Superconductivity, pseudogap and Mott transition

G. Sordi, P. Sémon, K. Haule, A.-M.S. Tremblay

In the cuprates, especially in the pseudogap regime, superconductivity is highly non-BCS. For example, there is local pair formation and a tendency to form inhomogeneous structures. In cuprates and in layered organic conductors, this can be a consequence of the intricate interplay between superconductivity, pseudogap and Mott transition. We provide a unified perspective on this interplay with the-two dimensional Hubbard model. In the strongly correlated regime that is relevant here, cluster generalizations of dynamical mean-field theory provide the best available tools. We use a continuous-time quantum Monte Carlo method as solver for the self-consistent 2 x 2 dynamical mean-field cluster. In the normal state, there is a first-order transition, with an associated large compressibility, that separates the pseudogap phase from the overdoped metal [1-3]. The metallic normal state close to the Mott insulator is unstable to d-wave superconductivity.  While superconductivity [4] can prevent the normal state phase transition, that transition leaves its mark on the dynamic properties of the superconducting phase.  For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states.  In the pseudogap regime, the dynamical mean-field superconducting transition temperature Tcd  does not scale with the order parameter. Tcd corresponds to the local pair formation temperature and is distinct from the pseudogap temperature.

Presented by A.-M.S. Tremblay

http://www.cap.ca/congress/2011/program/

The BCS theory of superconductivity is built on a normal metal where electrons feel a retarded attractive interaction mediated by lattice vibrations. In high temperature superconductors, the temperature dependence of the resistivity, photoemission and many other experiments reveal that the metallic state is unusual. Also, a slight change in carrier concentration transforms the superconducting state into an antiferromagnetic insulator at low temperature. That state remains insulator at higher temperature when there is no long-range order left. Such an insulating state, a Mott insulator, can be explained only if interactions are extremely strong and repulsive. In this talk, I summarize in simple terms a few of the results we have learned from numerical methods on the Mott insulator and on high-temperature superconductors.

First, it is shown that the underlying normal state, as described by the one-band Hubbard model, has critical behavior near optimal doping that is induced by Mott physics.[1] Mott physics can also lead, in the presence of very small orthorhombic distortions, to very large anisotropic response in the dynamics.[2] This provides an alternate route to stripes to explain the highly anisotropic behavior of transport properties observed close to half-filling. Finally, the relevance of Mott physics to superconductivity is discussed. It is shown that the zero temperature phase diagram of the cuprates obtained numerically is consistent with observation and leads to insights into the mechanism for pairing.[3] One can clearly identify retardation effects and associate the corresponding energy scales with short-range spin fluctuations.[4] These fluctuations are measured by neutron and optical spectroscopy probes.

1. G. Sordi, K. Haule, and A.-M.S. TREMBLAY
“Finite doping signatures of the Mott transition in the two-dimensional Hubbard model”
Phys. Rev. Lett. 104, 226402 (2010)

2. S. Okamoto, D. Sénéchal, M. Civelli, and A.-M.S. TREMBLAY
“Dynamical electronic nematicity from Mott Physics”
Phys. Rev. B 82, 180511(R) (2010)

3. S. S. Kancharla, M. Civelli, M. Capone, B. Kyung, D. Sénéchal, G. Kotliar, A.-M.S. Tremblay
“Anomalous superconductivity in doped Mott insulators”
Phys. Rev. B 77, 184516 (2008)

4. B. Kyung, D. Sénéchal and A.-M.S., Tremblay
“Pairing dynamics in strongly correlated superconductivity”
Phys. Rev. B 80, 205109 (2009)